Example

Example: Determining if the Relation {(3,6),(2,4),(1,2),(0,0),(1,2),(2,4),(3,6)}\{(-3, -6), (-2, -4), (-1, -2), (0, 0), (1, 2), (2, 4), (3, 6)\} is a Function

Consider the set of ordered pairs {(3,6),(2,4),(1,2),(0,0),(1,2),(2,4),(3,6)}\{(-3, -6), (-2, -4), (-1, -2), (0, 0), (1, 2), (2, 4), (3, 6)\}. To determine whether this relation is a function, observe if any xx-value (first coordinate) is matched with multiple yy-values (second coordinates). Each xx-value in this relation—specifically 3-3, 2-2, 1-1, 00, 11, 22, and 33—is unique and corresponds to exactly one yy-value, meaning the relation represents a true mathematical function. The function's domain is the explicit set of inputs: {3,2,1,0,1,2,3}\{-3, -2, -1, 0, 1, 2, 3\}. The range is the explicit set of outputs: {6,4,2,0,2,4,6}\{-6, -4, -2, 0, 2, 4, 6\}.

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Updated 2026-05-06

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